Apparatus for measuring an a.c. current in a cable

ABSTRACT

An apparatus for measuring alternating current in a conductor comprises first and second coils a 1   x , d 1   x  having substantially the same turns-area product and substantially parallel axes and located on the circumference of a circle with the first coil having its axis tangential to the circle and the second coil having its axis radially of the circle, and third and fourth coils a 1   y , d 1   y  also having substantially the same turns-area product and substantially parallel axes, the third and fourth coil means being located on the circumference of the same circle close to the first and second coil means respectively but having their axes orthogonal thereto. The coils are mounted on a support means configured to allow a conductor to be introduced into the centre of the said circle with the axis of the conductor normal to the plane containing the coils. The first and second coils are connected in series in anti-phase and the third and fourth coil means are connected in series in anti-phase, and the alternating current in the conductor is derived as a function of the voltages induced in the series-connected first and second coils and the series-connected third and fourth coils. Further coils are provided for interference suppression and signal enhancement.

This invention relates to an apparatus for measuring an alternatingcurrent flowing in an electric cable, for example an a.c. mains cable.

The present state of the art of measuring current in two or three coreround cables is described in U.S. Pat. No. 5,652,506. Part of the coilarrangement used in this prior apparatus is shown in FIG. 1.

Eight identical wire-wound coils are used in total in the previousarrangement. For clarity sake, only four of these are shown in FIG. 1.The four coils shown pick up the x component Hx of magnetic field onlyfrom the cable 10. The other four identical coils, not shown in thisdiagram, are located at the same centres as the four shown; however theyare wound in a plane which is normal to the plane of the four shown inorder to pick up the y component Hy of magnetic field only.

Coil 1 and coil 2 are the main pickup coils for the Hx component ofmagnetic field and are connected in phase addition. Coil 3 and coil 4are connected in phase opposition to coil 1 and coil 2. Coil 3 and coil4 are used only to reduce the pickup of stray magnetic fields from otherpossible interfering current sources which are external to the coilarrangement.

The magnetic field pick-up of coil 1 and coil 2 from the current sourceto be measured is larger than the pickup by coil 3 and coil 4 sincecoils 3 and 4 are further away from the current source. Thus, when theoutput from coils 3 and 4 is subtracted from coils 1 and 2 the result isnot zero. Therefore a voltage pickup proportional to the Hx component ofmagnetic field from the current source is present at the input to theamplifier AMP1.

For sources external and further away from the coil arrangement,however, the magnetic field created is much more uniform in magnitudeand direction in the vicinity of the coils and the pickup from coils 3and 4 almost completely cancels out the pickup from coils 1 and 2,significantly reducing any errors incurred due to other interferingcurrent sources in the vicinity of the apparatus.

At the output of the amplifier AMP1 there is a voltage Vx which isproportional to the magnetic field component Hx created by the currentflowing out in one conductor of the cable 10 and returning in the other.

The other four coils, picking up the Hy component, are connectedidentically to the four shown and are amplified separately by a similaramplifier AMP2, not shown. At the output of AMP2, therefore, a voltageVy exists which is proportional to the Hy component of magnetic field.

It is useful at this stage to examine the Hx and Hy components ofmagnetic field created by a current I flowing out in one conductor ofthe cable 10 and returning in a second conductor of the cable, located adistance d away from the first conductor, as shown in FIG. 2. For thepresent it is assumed that the two conductors do not twist or rotate asthey extend along the length of the cable.

Since the cable is round, no information is available as to theorientation angle θ of the coils to the conductors and θ is treated as avariable. Under these circumstances $\begin{matrix}{{Hx} = \frac{{Id}\quad\cos\quad\theta\quad\sin\quad\theta}{\pi\quad{r^{2}\left\lbrack {\left( {1 + \frac{d^{2}}{4r^{2}}} \right)^{2} - {\frac{d^{2}}{r^{2}}\sin^{2}\theta}} \right\rbrack}}} & {{Eq}\quad(1)} \\{{Hy} = \frac{{Id}\left( {{\sin^{2}\theta} - \frac{1}{2} - \frac{d^{2}}{8r^{2}}} \right)}{\pi\quad{r^{2}\left\lbrack {\left( {1 + \frac{d^{2}}{4r^{2}}} \right)^{2} - {\frac{d^{2}}{r^{2}}\sin^{2}\theta}} \right\rbrack}}} & {{Eq}\quad(2)}\end{matrix}$

Referring back to FIG. 1, if coil 1 is at an angle θ to thecurrent-carrying conductors, then coil 2, which is located diametricallyopposite to coil 1, has an angle θ+180° to the conductors and it is seenfrom equation (1) that Hx is identical for angles θ and θ+180°. Whencoils 1 and 2 are connected in phase addition, therefore, the pickupvoltage is double the pickup voltage of one of these coils on its own.

A similar analysis applies to the other coils picking up the Hycomponent of magnetic field as given by equation (2).

If the magnitude of the magnetic field |H| is then computed from the Hxand Hy components given by equations (1) and (2) respectively, thefollowing result is obtained: $\begin{matrix}{{H} = {\sqrt{{Hx}^{2} + {Hy}^{2}} = {\frac{Id}{2\quad\pi\quad r^{2}}\frac{1}{\sqrt{\left( {1 + \frac{d^{2}}{4r^{2}}} \right)^{2} - {\frac{d^{2}}{r^{2}}\sin^{2}\theta}}}}}} & {{Eq}.\quad(3)}\end{matrix}$

Now Vx, the output voltage of AMP1, is proportional to Hx, and Vy, theoutput voltage of AMP2, is proportional to Hy.

V is evaluated from Vx and Vy, as follows: $\begin{matrix}{V = {\sqrt{{Vx}^{2} + {Vy}^{2}} = {{K{H}} = {\frac{KId}{2\quad\pi\quad r^{2}}\frac{1}{\sqrt{\left( {1 + \frac{d^{2}}{4r}} \right)^{2} - {\frac{d^{2}}{r^{2}}\sin^{2}\theta}}}}}}} & {{Eq}.\quad(4)}\end{matrix}$

Where K is a constant that depends on the area and number of the coilturns and the amplifier gain.

The computed voltage V is a maximum at θ=90° and is given by$\begin{matrix}{{V\quad\max} = \frac{KId}{2\quad\pi\quad{r^{2}\left( {1 - \frac{d^{2}}{4r^{2}}} \right)}}} & {{Eq}\quad(5)}\end{matrix}$and V is a minimum when θ=0° $\begin{matrix}{{V\quad\min} = \frac{KId}{2\quad\pi\quad{r^{2}\left( {1 + \frac{d^{2}}{4r^{2}}} \right)}}} & {{Eq}\quad(6)}\end{matrix}$

The average value of V is approximately $\begin{matrix}{V = \frac{KId}{2\quad\pi\quad r^{2}}} & {{Eq}\quad(7)}\end{matrix}$

Equation (7) is the equation used to evaluate the current I, since K andr are known, and d can be estimated fairly accurately in the previouslypatented technique.

For I fixed, however, there is an inherent variation in the measuredvoltage V as the coil positions around the cable vary as indicated byequations (5) and (6). The maximum variation from equation (7) dependson the value of d²/4r². For d/r=½ there is a maximum variation (error)of ±6.3%. For d/r<½ the variation (error) is smaller in theory. Inpractice, however, the best accuracy that can be achieved with thisprevious apparatus, in round cables, is of the order of ±11%.

The reason the performance is worse than indicated by equation (4) isprimarily due to the fact that in round cables the conductors twist asthey extend along the length of the cable. It was assumed in derivingequation (4) that the conductors stay parallel and straight along thecable.

Equation (4) indicates that the maximum pickup occurs when the angleθ=90° and the minimum pickup occurs when 0=0°. It is found that thiseffect reverses itself when the conductors are twisted beyond a certainlimit, causing the maximum pickup to occur at θ=0° and the minimum tooccur at θ=90°. The variation in pickup of this previous apparatus asthe coils move round the twisted conductors depends on the rate oftwist, the spacing d, and the distance to the coils r.

If V is computed from V=√{square root over (V_(x) ²+V_(y) ²))} for thecoil arrangement shown in FIG. 1, then variations in readings as thecoils rotate round the cable vary from cable to cable but can exceed±15%.

The coil arrangement shown in FIG. 1 is therefore limited in itsaccuracy, and it is an object of the invention to provide a newapparatus which is capable of giving greater accuracy.

This object is met by the invention claimed in claim 1. Preferredembodiments of the invention are claimed in the dependent claims.

In this specification the axis of a coil means that direction relativeto the coil which, when orientated parallel to the direction of afluctuating magnetic field passing through the coil, would provide themaximum induced voltage in the coil for that magnetic field.

An embodiment of the invention will now be described, by way of example,with reference to the accompanying drawings, in which:

FIG. 1, previously described, shows part of a prior art apparatus.

FIG. 2 is a diagram to assist in understanding the operation andlimitations of the prior art.

FIG. 3 is a schematic diagram of the coil arrangement of a basicembodiment of the present invention.

FIG. 4 is a diagram of the embodiment of FIG. 3 illustrating the effectof an interfering source.

FIG. 5 is a further development of the embodiment of FIG. 3.

FIG. 6 shows an embodiment of the invention with interferencesuppression.

FIG. 7 is a circuit diagram of the embodiment of FIG. 6.

FIG. 8 shows an alternative construction for the orthogonal coils ofFIG. 6.

As described, coils 1 and 2 of the apparatus shown in FIG. 1 pick up theHx component of magnetic field. These coils are also present in theapparatus shown in FIG. 3, which is a circuit diagram of the coilarrangement of a basic embodiment of the present invention, but they arereferred to there as coils a_(x) and b_(x). The apparatus of FIG. 3 alsoincludes two further coils c_(x) and d_(x) which also pick up the Hxcomponent of magnetic field. These two further coils c_(x) and d_(x) arelocated at the same distance as coils a_(x) and b_(x) from the centre ofthe cable 10 but are located above and below the cable so that a linejoining coil c_(x) to coil d_(x) is at an angle of 90° to a line joiningcoil a_(x) and coil b_(x). Thus all four coils a_(x) to d_(x) lie in aplane which is perpendicular to the axis of the cable 10 on thecircumference of a notional circle of radius r whose centre is coaxialwith the cable 10. All four coils a_(x) to d_(x) have substantiallyparallel axes; thus the axes of coils a_(x) and b_(x) are tangential tothe notional circle while the axes of coils c_(x) and d_(x) extendradially of the notional circle. All four coils a_(x) to d_(x) havesubstantially the same turns-area product

Thus, with reference to FIG. 2, if coil a_(x) is at an angle θ to thetwo conductors of the cable 10, then coil d_(x) is at 90°+θ, coil b_(x)is at 180°+θ and coil c_(x) is at 270°+θ. The advantage of thisapparatus over the previous one, if the coils are connected in series inthe correct polarity in the manner to be described, is that the pickuprepeats itself every 90° of rotation and so the pickup at θ=0° and θ=90°are identical. In the previous apparatus maximum variation betweenreading occurred at θ=0° and 90°.

The variation in pickup of the Hx component of magnetic field thatoccurs at each of the four coils a_(x) to d_(x) located round a parallelpair of conductors, as shown in FIG. 3, is now examined with the use ofequation (1).

If coil a_(x) is at an angle θ to the conductor pair then Hx at coila_(x) is given by equation (1) as: $\begin{matrix}{{{Hx}\left( a_{x} \right)} = \frac{{Id}\quad\cos\quad\theta\quad\sin\quad\theta}{\pi\quad{r^{2}\left\lbrack {\left( {1 + \frac{d^{2}}{4r^{2}}} \right)^{2} - {\frac{d^{2}}{r^{2}}\sin^{2}\theta}} \right\rbrack}}} & {{Eq}\quad(8)}\end{matrix}$

For coil d_(x) its angle is 90+θ to the conductors and the Hx componentthere, again from equation (1), is $\begin{matrix}{{{Hx}\left( d_{x} \right)} = {- \frac{{Id}\quad\cos\quad\theta\quad\sin\quad\theta}{\pi\quad{r^{2}\left\lbrack {\left( {1 + \frac{d^{2}}{4r^{2}}} \right)^{2} - {\frac{d^{2}}{r^{2}}\sin^{2}\theta}} \right\rbrack}}}} & {{Eq}\quad(9)}\end{matrix}$

For coil b_(x) its angle is 180°+θ to the conductors and therefore$\begin{matrix}{{{Hx}\left( b_{x} \right)} = \frac{{Id}\quad\cos\quad\theta\quad\sin\quad\theta}{\pi\quad{r^{2}\left\lbrack {\left( {1 + \frac{d^{2}}{4r^{\quad}}} \right)^{2} - {\frac{d^{2}}{r^{2}}\sin^{2}\theta}} \right\rbrack}}} & {{Eq}\quad(10)}\end{matrix}$

For coil (c_(x)) its angle is 270°+θ to the conductors giving$\begin{matrix}{{{Hx}\left( c_{x} \right)} = {- \frac{{Id}\quad\cos\quad\theta\quad\sin\quad\theta}{\pi\quad{r^{2}\left\lbrack {\left( {1 + \frac{d^{2}}{4r^{2}}} \right)^{2} - {\frac{d^{2}}{r^{2}}{\cos^{2}}^{\quad}\theta}} \right\rbrack}}}} & {{Eq}\quad(11)}\end{matrix}$

Coils a_(x) to d_(x) are all connected in series, as shown in FIG. 3, inthe following polarities. Coils a_(x) and b_(x) have an in-phaseconnection and coils c_(x) and d_(x) are connected in anti-phase tocoils a_(x) and b_(x) so that the voltage V(x) induced in the seriesconnection of coils a_(x) to d_(x) is proportional to:Hx(a_(x))+Hx(b_(x))−Hx(c_(x))−Hx(d_(x)).

Substituting for the values of these magnetic fields from equations (8),(9), (10), and (11) and simplifying gives $\begin{matrix}{{{{Hx}\left( a_{x} \right)} + {{Hx}\left( b_{x} \right)} - {{Hx}\left( c_{x} \right)} - {{Hx}\left( d_{x} \right)}} = {\frac{4{Id}}{\pi\quad r^{2}}\frac{\cos\quad\theta\quad\sin\quad{\theta\left( {1 + \frac{d^{4}}{16r^{4}}} \right)}}{\left\lbrack {\left( {1 + \frac{d^{2}}{4{r^{2}}^{\quad}}} \right)^{2} - {\frac{d^{2}}{r^{2}}\cos^{2}\theta}} \right\rbrack\left\lbrack {\left( {1 + \frac{d^{2}}{4r^{2}}} \right)^{2} - {\frac{d^{2}}{r^{2}}\sin^{2}\theta}} \right\rbrack}}} & {{Eq}\quad(12)}\end{matrix}$

The arrangement of FIG. 3 also includes four further coils a_(y), b_(y),c_(y) and d_(y) each having substantially the same turns-area product aseach of the coils a_(x) to d_(x). Each coil a_(y) to d_(y) is placed, asfar as is physically practical, at the same location as a correspondingone of the coils a_(x) to d_(x), but its axis is rotated through 90° sothat the axes of the coils a_(y) and b_(y) are tangential to thenotional circle and the axes of the coils c_(y) and d_(y) extendradially of the notional circle. Thus four pairs a_(x)/a_(y),b_(x)/b_(y), c_(x)/c_(y) and d_(x)/d_(y) of closely positioned coils arepresent with the coils in each pair having substantially orthogonalaxes. This close positioning of the pairs of coils a_(x)/a_(y), etc. atthe same location can be achieved, for example, using orthogonal pairsof coils as shown in FIG. 9 of U.S. Pat. No. 5,652,506 but analternative construction using PCB technology will be described later.As will be evident to the reader, each of the coils a_(y) to d_(y) isorientated to pick up the y component Hy of the magnetic field generatedby the cable 10 at the respective location.

Let Hy(a_(y)) be the y component of magnetic field picked up by the coila_(y).

Let Hy(b_(y)) be the y component of magnetic field picked up by the coilb_(y).

Let Hy(c_(y)) be the y component of magnetic field picked up by the coilc_(y).

Let Hy(d_(y)) be the y component of magnetic field picked up by the coild_(y).

From equation (2) $\begin{matrix}{{{Hy}\left( a_{y} \right)} = {\frac{Id}{\pi\quad r^{2}}\frac{\left\lbrack {{\sin^{2}\theta} - \frac{1}{2} - \frac{d^{2}}{8r^{2}}} \right\rbrack}{\left\lbrack {\left( {1 + \frac{d^{2}}{4r^{2}}} \right)^{2} - {\frac{d^{2}}{r^{2}}\sin^{2}\theta}} \right\rbrack}}} & {{Eq}\quad(13)} \\{{{Hy}\left( d_{y} \right)} = {\frac{Id}{\pi\quad r^{2}}\frac{\left\lbrack {{\cos^{2}\theta} - \frac{1}{2} - \frac{d^{2}}{8r^{2}}} \right\rbrack}{\left\lbrack {\left( {1 + \frac{d^{2}}{4r^{2}}} \right)^{2} - {\frac{d^{2}}{r^{2}}\cos^{2}\theta}} \right\rbrack}}} & {{Eq}\quad(14)} \\{{{Hy}\left( b_{y} \right)} = {\frac{Id}{\pi\quad r^{2}}\frac{\left\lbrack {{\sin^{2}\theta} - \frac{1}{2} - \frac{d^{2}}{8r^{2}}} \right\rbrack}{\left\lbrack {\left( {1 + \frac{d^{2}}{4r^{2}}} \right)^{2} - {\frac{d^{2}}{r^{2}}\sin^{2}\theta}} \right\rbrack}}} & {{Eq}\quad(15)} \\{{{Hy}\left( c_{y} \right)} = {\frac{Id}{\pi\quad r^{2}}{\frac{\left\lbrack {{\cos^{2}\theta} - \frac{1}{2} - \frac{d^{2}}{8r^{2}}} \right\rbrack}{\left\lbrack {\left( {1 + \frac{d^{2}}{4r^{2}}} \right)^{2} - {\frac{d^{2}}{r^{2}}\cos^{2}\theta}} \right\rbrack}.}}} & {{Eq}\quad(16)}\end{matrix}$

These four coils a_(y to d) _(y) picking up the Hy component of magneticfield are connected in series with the same polarities as the four coilsa_(x) to d_(y) picking up the Hx component; i.e. coils a_(y) and b_(y)are connected in phase and coils c_(y) and d_(y) are connected inantiphase to coils a_(y) and b_(y). To avoid over-complicating FIG. 3the connections between the coils a_(y) to d_(y) are not shown in thatfigure.

A voltage V(y) is therefore induced in the series connectionproportional toHy(a_(y))+Hy(b_(y))−Hy(c_(y))−Hy(d_(y)).

Substituting for the values of these magnetic fields from equation (13)to (16) and simplifying gives $\begin{matrix}{{{{Hy}{\left( a_{y} \right) + {{Hy}\left( b_{y} \right)}}} - {{Hy}\left( c_{y} \right)} - {{Hy}\left( d_{y} \right)}} = {\frac{2{Id}}{\pi\quad r^{2}}{\frac{\left( {{\sin^{2}\theta} - {\cos^{2}\theta}} \right)\left( {1 - \frac{d^{4}}{16r^{4}}} \right)}{\left\lbrack {\left( {1 + \frac{d^{2}}{4r^{2}}} \right)^{2} - {\frac{d^{2}}{r^{2}}\sin^{2}\theta}} \right\rbrack\left\lbrack {\left( {1 + \frac{d^{2}}{4r}} \right)^{2} - {\frac{d^{2}}{r^{2}}\cos^{2}\theta}} \right\rbrack}.}}} & {{Eq}\quad(17)}\end{matrix}$

V is now evaluated as: $\begin{matrix}\begin{matrix}{V = \sqrt{{V(x)}^{2} + {V(y)}^{2}}} \\{= {K\sqrt{\left\lbrack {{{Hx}\left( a_{x} \right)} + {{Hx}\left( b_{x} \right)} - {{Hx}\left( c_{x} \right)} - {{Hx}\left( d_{x} \right)}} \right\rbrack^{2} + \left\lbrack {{{Hy}\left( a_{y} \right)} + {{Hy}\left( b_{y} \right)} - {{Hy}\left( c_{y} \right)} - {{Hy}\left( d_{y} \right)}} \right\rbrack^{2}}}}\end{matrix} & {{Eq}\quad(18)}\end{matrix}$where K is a constant, as before.

Substituting in equation (18) from equations (12) and (17), andsimplifying, gives $\begin{matrix}{V = {\frac{2{KdI}}{\pi\quad r^{2}}\frac{1}{\sqrt{\left( {1 - \frac{d^{4}}{16r^{4}}} \right)^{2} + {\frac{d^{4}}{r^{4}}\sin^{2}{\theta cos}^{2}\theta}}}}} & {{Eq}\quad(19)}\end{matrix}$

The minimum value of V occurs when θ=45° and this value is given by$\begin{matrix}{V_{MIN} = \frac{2{KdI}}{\pi\quad{r^{2}\left( {1 + \frac{d^{4}}{16r^{4}}} \right)}}} & {{Eq}\quad(20)}\end{matrix}$

The maximum value of V occurs when θ=0° or θ=90° and this maximum valueis given by $\begin{matrix}{V_{MAX} = \frac{2{KdI}}{\pi\quad{r^{2}\left( {1 - \frac{d^{4}}{16r^{4}}} \right)}}} & {{Eq}\quad(21)}\end{matrix}$

The mean value is approximately $\begin{matrix}{V_{AV} = \frac{2{KdI}}{\pi\quad r^{2}}} & {{Eq}\quad(22)}\end{matrix}$

Except for a factor of four, equation (22) of the new apparatus isexactly the same as equation (7) of the previous apparatus. However, thevariation from maximum to minimum of the previous apparatus as thesensor is rotated depends on the magnitude of d²/4r², whereas for thenew coil arrangement it depends on the magnitude of d⁴/16r⁴. Thus, ford/r=½ the reading varies by ±6.3% for the previous apparatus whereas thenew apparatus, with d/r=½, varies by only ±0.4%.

The improvement using the new coil arrangement as given by equation (19)compared to the previous apparatus as given by equation (4) is strictlytrue only for conductors which do not twist as they extend along thelength of the cable. However, the new apparatus is far less prone toerrors caused by cable rotation or conductor twisting with variations of<2% recorded in V as the cable is rotated by 360° for this new coilarrangement. The previous apparatus records variations of 15% or largerwhere the same cable is rotated in the jaws of the instrument.

In the previous coil arrangement, as shown in FIG. 1, coil 3 and coil 4are connected in anti-phase with coil 1 and coil 2, and their purpose isto reduce the pickup of interference from the other current sources inthe vicinity of the meter. The interference pickup of the coilarrangement shown in FIG. 3 is now examined with reference to FIG. 4.

FIG. 4 shows the coils a_(x) to d_(x) located on the circle of radius r.Also shown is a cable 10 carrying a current I located at two possiblepositions, position A or position B. Position A is the location of thecable when a measurement of its current I is made. Position B shows thesame cable, located a distance r_(I) from the centre of the circle,carrying the same current I but exterior to the coil arrangement, whereit is acting as an interfering source. The interference suppression S ofthe coil arrangement is defined as: $\begin{matrix}{S = \frac{{Pickup}\quad{in}\quad{position}\quad B}{{Pickup}\quad{in}\quad{position}\quad A}} & {{Eq}.\quad(23)}\end{matrix}$

The smaller the value of S the better the suppression. The pickup inposition A is given by equation (22)${{Pickup}\quad{in}\quad{position}\quad A} = \frac{2{KdI}}{\pi\quad r^{2}}$

It may be shown that the pickup in position B is given by$\begin{matrix}{{{Pickup}\quad{in}\quad{position}\quad B} = \frac{6r^{2}{KdI}}{\pi\left( {r_{I}^{4} - r^{4}} \right)}} & {{Eq}.\quad(24)} \\{{{Therefore}\quad S} = \frac{3r^{4}}{r_{I}^{4}\left( {1 - \frac{r^{4}}{r_{I}^{4}}} \right)}} & {{Eq}.\quad(25)}\end{matrix}$

It is seen from equation (25) that the smaller the value of$\frac{r}{r_{I}}$the better the suppression.

If it is assumed, due to coil and apparatus housings, that the closestan interference source can get to the coil arrangement is r_(I)=2r, thenthe maximum value of S from equation (25) is S=0.2 or 20%. As theinterfering source moves further away S decreases fairly rapidly, withS=4% for r_(I)=3r and S=1% for r_(I)=4r. This maximum interference valueof 20% is in general unacceptable and is reduced significantly byemploying the following technique.

It is noted from equation (24) that the interference pickup is primarilyproportional to r² where r is the distance of the coils from the centre.Consider therefore the situation as shown in FIG. 5. In thisarrangement, two sets of coils are used to pickup the Hx component ofmagnetic field, an inner set a1 _(x) to d1 _(x) located at 90° intervalsaround the circumference of a circle of radius r, and an outer set a2_(x) to d2 _(x) located at 90° intervals around the circumference of acircle of radius r₂ coaxial with the first circle. The four inner coilsa1 _(x) to d1 _(x) correspond to the coils a_(x) to d_(x) shown in FIG.3, and are connected in series in the same way, and the four outer coilsa2 _(x) to d2 _(x) are also connected in series in the manner shown inFIG. 3. Each outer coil a2 _(x) to d2 _(x) is located on the same radialline as a corresponding one of the inner coils a1 _(x) to d1 _(x) andall eight coils have substantially parallel axes and substantially thesame area-turns product.

Let V_(1x) be the pickup by the inner set of coils from the interferingsource at distance r_(I) which is given by equation (24) with r=r₁.$\begin{matrix}{V_{1x} = \frac{6r_{1}^{2}{KdI}}{\pi\left( {r_{I}^{4} - r_{1}^{4}} \right)}} & {{Eq}.\quad(26)}\end{matrix}$

Let V_(2x) be the pickup by the outer set of coils from the sameinterfering source. $\begin{matrix}{V_{2x} = \frac{6r_{2}^{2}{KdI}}{\pi\left( {r_{I}^{4} - r_{2}^{4}} \right)}} & {{Eq}.\quad(27)}\end{matrix}$

In order to reduce the pickup from this interfering source a fraction,r1²/r2², of the outer voltage is subtracted from the inner voltage togive Vx, where $\begin{matrix}{V_{x} = {V_{1x} - {\frac{r_{1}^{2}}{r_{2}^{2}}V_{2x}}}} & {{Eq}.\quad(28)}\end{matrix}$

Substituting for V_(1x) and V_(2x) from equations (26) and (27) gives${Vx} = {\frac{6r_{1}^{2}{KdI}}{\pi\left( {r_{I}^{4} - r_{1}^{4}} \right)} - {\frac{r_{1}^{2}}{r_{2}^{2}}\left\lbrack \frac{6r_{2}^{2}{KdI}}{\pi\left( {r_{I}^{4} - r_{2}^{4}} \right)} \right\rbrack}}$

Simplifying gives $\begin{matrix}{{Vx} = {\frac{6{KdI}}{\pi}\frac{r_{1}^{2}}{r_{I}^{8}}\frac{\left( {r_{1}^{4} - r_{2}^{4}} \right)}{\left( {1 - \frac{r_{1}^{4}}{r_{I}^{4}}} \right)\left( {1 - \frac{r_{2}^{4}}{r_{I}^{4}}} \right)}}} & {{Eq}.\quad(29)}\end{matrix}$

Since this is the pickup from the interfering source at distance r_(I),call this voltage V_(xB). $\begin{matrix}{{i.e.\quad V_{xB}} = {\frac{6{KdI}}{\pi}\frac{r_{1}^{2}}{r_{I}^{8}}\frac{\left( {r_{1}^{4} - r_{2}^{4}} \right)}{\left( {1 - \frac{r_{1}^{4}}{r_{I}^{4}}} \right)\left( {1 - \frac{r_{2}^{4}}{r_{I}^{4}}} \right)}}} & {{Eq}.\quad(30)}\end{matrix}$

Consider now the pickup from the same current source when it is locatedin the measurement position (in the centre of the coil system) when thetotal voltage pickup is again computed from equation (28).

The pickup voltage V_(1x) of the inner coil set is given by equation(22) with r=r₁. $V_{1x} = \frac{2{KdI}}{\pi\quad r_{1}^{2}}$

Similarly, the pickup voltage V_(2x) of the outer set is given byequation (22) with r=r2. $V_{2x} = \frac{2{KdI}}{\pi\quad r_{2}^{2}}$

The total pickup voltage V_(xa) with the cable in the measurementposition is obtained by substituting these values of V_(1x) intoequation (28) $\begin{matrix}\begin{matrix}{V_{xA} = {\frac{2{KdI}}{\pi\quad r_{1}^{2}} - {\frac{r_{1}^{2}}{r_{I}^{2}}\frac{2{KdI}}{\pi\quad r_{2}^{2}}}}} \\{V_{xA} = {\frac{2{KdI}}{\pi}\frac{\left( {r_{2}^{4} - r_{1}^{4}} \right)}{r_{1}^{2}r_{2}^{4}}}}\end{matrix} & {{Eq}.\quad(31)}\end{matrix}$

The interference ratio S, given by equation (23) for this new apparatuswith inner and outer sets of coils, is$S = {\frac{VxB}{VxA} = {\frac{6{{KdIr}\quad}_{1}^{2}\quad\left( {r_{1}^{4} - r_{2}^{4}} \right)}{\pi\quad{r_{I}^{8}\left( {1 - \frac{r_{1}^{4}}{r_{I}^{4}}} \right)}\left( {1 - \frac{r_{2}^{4}}{r_{I}^{4}}} \right)} \times \frac{r_{1}^{2}r_{2}^{4}\pi}{\left( {r_{2}^{4} - r_{1}^{4}} \right)\quad 2{KdI}}}}$

Simplifying gives $\begin{matrix}{S = \frac{3r_{1}^{4}r_{2}^{4}}{{r_{I}^{8}\left( {1 - \frac{r_{1}^{4}}{r_{I}^{4}}} \right)}\left( {1 - \frac{r_{2}^{4}}{r_{I}^{4}}} \right)}} & {{Eq}.\quad(32)}\end{matrix}$

If the inner set on its own had only been used, the interference ratiofor that arrangement was given previously by equation (25) with r=r₁giving $\begin{matrix}{{S\quad\left( {r_{1}{only}} \right)} = \frac{3r_{1}^{4}}{r_{I}^{4}\left( {1 - \frac{r_{1}^{4}}{r_{I}^{4}}} \right)}} & {{Eq}.\quad(33)}\end{matrix}$

The interference ratio S of the new apparatus as given by equation (32)is smaller than that for the inner set on its own, as given by equation(33), by the factor$\frac{r_{2}^{4}}{r_{I}^{4}}\frac{1}{\left( {1 - \frac{r_{2}^{4}}{r_{I}^{4}}} \right)}$

For example when r=2r₂ this factor is 0.067, causing a reduction ininterference pickup by a factor of 16 approximately. Thus, the worstinterference drops from 20% for the inner set on its own to 1.25% whenthe inner and outer voltages are subtracted in the ratio given byequation (28) i.e. r₁ ²/r₂ ². When the interfering sources are further,away the reduction factor is even larger. The subtraction of the factorr₁ ²/r₂ ² of the outer voltage from the inner voltage may be implementedwith a resistor divider network or as part of an amplifier input stageas will be described with reference to FIG. 7.

The same considerations apply to the coils detecting the Hy component ofthe magnetic field.

FIG. 6 is a plan view of an embodiment of the invention incorporatinginterference suppression as described above, and FIG. 7 is its circuitdiagram.

In FIG. 6, the four inner coils a1 _(x) to d1 _(x) are mounted on a“C-shaped” insulating motherboard 20 at 90° intervals around thecircumference of a notional circle of radius r₁, and the four outercoils a2 _(x) to d2 _(x) are mounted on the motherboard 20 at 90°intervals around the circumference of a notional circle of radius r₂,the two circles being concentric. All eight coils a1 _(x) to d1 _(x) anda2 _(x) to d2 _(x) have substantially the same area-turns product andsubstantially parallel axes and are located substantially in a commonplane.

Also mounted on the motherboard 20 are eight further coils, an inner setof coils a1 _(y) to d1 _(y) and an outer set of coils a2 _(y) to d2_(y). The coils a1 _(y) to d1 _(y) and a2 _(y) to d2 _(y) havesubstantially parallel axes and substantially the same turns-areaproduct as the coils a1 _(x) to d1 _(x) and a2 _(x) to d2 _(x). However,their axes are normal to the axes of the coils a1 _(x) to d1 _(x) and a2_(x) to d2 _(x). Thus each coil a1 _(x) to d1 _(x) and a2 _(x) to d2_(x) forms an orthogonal pair of coils with a corresponding one of thecoils a1 _(y) to d1 _(y) and a2 _(y) to d2 _(y), wherein in eachorthogonal pair the two coils, e.g. the pair of coils a1 _(x) and a1_(y), are at substantially the same location on the motherboard 20,insofar as that is physically practical using the chosen technology, butthe axis of one of the coils is rotated through 90° relative to theother coil so that the axis of one coil is tangential to the notionalcircle on which it lies while the axis of the other coil extendsradially of the same circle. Thus the motherboard 20 bears eightorthogonal pairs of coils, four inner pairs a1 _(x)/a1 _(y), b1 _(x)/b1_(y), c1 _(x)/c1 _(y) and d1 _(x)/d1 _(y) and four outer pairs a2_(x)/a2 _(y), b2 _(x)/b2 _(y), 2 _(x)/c2 _(y) and d2 _(x)/d2 _(y). Asmentioned above, this close positioning of the pairs of coils a1 _(x)/a1_(y), b1 _(x)/b1 _(y) . . . etc. at the substantially same physicallocation can be achieved using orthogonal pairs of coils as shown inFIG. 9 of U.S. Pat. No. 5,652,506.

The gap 22 in the C-shaped motherboard 20 allows a cable 10, not shownin FIG. 6, to be introduced into the support so as to be positioned atthe point P at the centre of the circles of radius r₁ and r₂, the cableextending normal to the plane containing the coils (i.e. normal to theplane of FIG. 6). In practice the motherboard 20 and coils mountedthereon will be accommodated in a housing (not shown) which couldincorporate a clamp or other mechanical device to locate the cable atthe point P. Clearly, each of the coils a1 _(x) to d1 _(x) and a2 _(x)to d2 _(x) is orientated to pick up the x component Hx of the magneticfield generated by the cable 10, while each of the coils a1 _(y) to d1_(y) and a2 _(y) to d2 _(y) is orientated to pick up the y component Hyof the magnetic field generated by the cable 10.

The coils are connected as shown in FIG. 7:

-   -   Coils a1 _(x) and b1 _(x) are connected in phase with one        another and coils c1 _(x) and d1 _(x), although connected in        phase with one another, are connected in anti-phase to coils a1        _(x) and b1 _(x) to give an overall output voltage V_(1x) at the        input to a resistor R_(1x).    -   Coils a2 _(x) and b2 _(x) are connected in phase with one        another and coils c2 _(x) and d2 _(x), although connected in        phase with one another, are connected in anti-phase to coils a2        _(x) and b2 _(x) to give an overall output voltage V_(2x) at the        input to a resistor R_(2x) (the voltage V_(2x) is shown minus        because the entire series connection of coils a2 _(x) to d2 _(x)        is connected in reverse polarity to coils a1 _(x) to d1 _(x)).    -   Coils a1 _(y) and b1 _(y) are connected in phase with one        another and coils c1 _(y) and d1 _(y), although connected in        phase with one another, are connected in anti-phase to coils a1        _(y) and b1 _(y) to give an overall output voltage V_(1y) at the        input to a resistor R_(1y).    -   Coils a2 _(y) and b2 _(y) are connected in phase with one        another and coils c2 _(y) and d2 _(y), although connected in        phase with one another, are connected in anti-phase to coils a2        _(y) and b2 _(y) to give an overall output voltage V_(2y) at the        input to a resistor R_(2y) (again, the voltage V_(2y) is shown        minus because the entire series connection of coils a2 _(y) to        d2 _(y) is connected in reverse polarity to coils a1 _(y) to d1        _(y)).

The resistors R_(1x) and R_(2x) are connected in common to the negativeinput to an amplifier AMP1 and are chosen such that:$\frac{R_{1x}}{R_{2x}} = \left( \frac{r_{1}^{2}}{r_{2}^{2}} \right)$

V_(out)x is therefore given as${V_{out}x} = {\frac{- R}{1 + {{j\omega}\quad{cR}}}\left( {\frac{V_{1x}}{R_{1x}} - \frac{V_{2x}}{R_{2x}}} \right)}$

For the frequency range of interest, jωRc is much greater than 1,therefore $\begin{matrix}{{V_{out}x} = {\frac{- 1}{{j\omega}\quad c}\left( {\frac{V_{1x}}{R_{1x}} - \frac{V_{2x}}{R_{2x}}} \right)}} \\{= {\frac{j}{\omega\quad{cR}_{1x}}\left( {V_{1x} - \frac{R_{1x}V_{2x}}{R_{2x}}} \right)}}\end{matrix}$

Similarly, the resistors R_(1y) and R_(2y) are connected in common tothe negative input to an amplifier AMP2 and are chosen such that:$\frac{R_{1y}}{R_{2y}} = \left( \frac{r_{1}^{2}}{r_{2}^{2}} \right)$

V_(out)y is therefore given as${V_{out}y} = {\frac{- R}{1 + {{j\omega}\quad{cR}}}\left( {\frac{V_{1y}}{R_{1y}} - \frac{V_{2y}}{R_{2y}}} \right)}$

For the frequency range of interest, jωRc is much greater than 1,therefore $\begin{matrix}{{V_{out}y} = {\frac{- 1}{{j\omega}\quad c}\left( {\frac{V_{1y}}{R_{1y}} - \frac{V_{2y}}{R_{2y}}} \right)}} \\{= {\frac{j}{\omega\quad c\quad R_{1y}}\left( {V_{1y} - \frac{R_{1y}V_{2y}}{R_{2y}}} \right)}}\end{matrix}$

Finally, the current flowing in the cable is calculated in a processor30 by evaluatingV _(out)=√{square root over ((V _(out) x)²+(V _(out) y)²)}and the measured current displayed on a display device such as an LCDpanel (not shown). The connections between the various coils can beeffected by using conductive tracks (not shown) laid down on themotherboard 20 using printed circuit board (PCB) technology. Theamplifiers AMP1 and AMP2, as well as the processor 30, can be formed byintegrated circuit technology and the IC chips located on themotherboard 20 or elsewhere in the device housing.

A total of 16 coils are used in this embodiment and ideally thetuns-area product of these coils should be the same to within 1% atleast to obtain accurate results. The cost of 16 wirewound coilsaccurate to this tolerance could be too expensive for many applications.Planar magnetic printed circuit board coils are a lot cheaper and moreaccurate to manufacture. However, for a true implementation of theapparatus shown in FIGS. 6 and 7, in each pair of orthogonal coils thegeometric centre of each of the coils a1 _(x), b1 _(x), etc. picking upthe Hx component should be located at the same position as the geometriccentre of the corresponding coil a1 _(y), b1 _(y), etc. picking up theHy component. This is possible using the technique shown in FIG. 9 ofU.S. Pat. No. 5,652,506 but not with planar magnetic coils as the tracksare confined to one plane and it is not possible with present daytechniques to simultaneously have tracks on orthogonal planes in thesame PCB. However, a slight compromise with planar magnetic printedcircuit board coils works very well and this arrangement is shown inFIGS. 8(a) to 8(c). FIG. 8 actually shows the PCB implementation of thetwo orthogonal coil pairs a1 _(x)/a1 _(y) and a2 _(x)/a2 _(y)) but thesame principle is applicable to the two orthogonal coil pairs on thesame radius at each of the other three quadrants of the motherboard 20.

The coils a1 _(y) and a2 _(y) are substantially identical and each isformed as a conductive track 40 on an insulating substrate 42. Althoughonly one side of the substrate is seen in FIG. 8(c), tracks 40 areformed on each opposite surface of the substrate and connected in seriesthrough a central via hole 44. Both tracks 40 form the coil whoseopposite ends are connected to respective solder pads 46 formed on tabsextending down from the main body of the substrate 42.

By contrast, each coil a1 _(x) and a2 _(x) is formed in two parts.Considering coil a1 _(x), it is formed in two parts a1 _(x)(1) and a1_(x)(2). The parts a1 _(x)(1) and a1 _(x)(2) are formed as conductivetracks 50 on respective insulating substrates 52. However, each of theparts a1 _(x)(1) and a1 _(x)(2) has a turns-area product half that ofthe coil a1 _(y). This can be achieved by providing double the number ofturns on the coil a1 _(y) than the number on parts a1 _(x)(1) and a1_(x)(2).

Similarly, the coil a2 _(x) is formed in two parts a2 _(x)(1) and a2_(x)(2), again formed as conductive tracks 50 on respective insulatingsubstrates 52 and each having a turns-area product half that of the coila2 _(y). Actually, in this embodiment the parts a1 _(x)(1) and a2_(x)(1) are formed on one common substrate 52 and likewise the parts a1_(x)(2) and a2 _(x)(2) are formed on another common substrate 52, butthis is not necessary.

The substrates 42, 52 are mounted upstanding vertically in themotherboard 20 by inserting the solder tabs 46, 56 into slots in themotherboard and soldered to tracks on the motherboard. The arrangementis as shown in FIG. 8(a). The coil a1 _(y) is embraced on each side bythe coils a1 _(x)(1) and a1 _(x)(2) normal thereto, and the coil a2 _(y)is embraced on each side by the coils a2 _(x)(1) and d2 _(x)(2) normalthereto. The solder tabs 56 are connected by conductive tracks on themotherboard 20 to connect the coils a1 _(x)(1) and a1 _(x)(2) in seriesin phase to form the coil a1 _(x) and the coils a2 _(x)(1) and a2_(x)(2) in series in phase to form the coil a2 _(x). Since the coilparts a1 _(x)(1) and a1 _(x)(2) combined have the same turns-areaproduct as the coil a1 _(y) and are equally spaced at either end of coila1 _(y), as a pair they have the same geometrical centre as coil a1_(y). Similarly, as a pair the coil parts a2 _(x)(1) and a2 _(x)(2) theyhave the same geometrical centre as coil a2 _(y). The remainingconnections are as shown in FIG. 7.

Modifications of the above embodiment are possible. For example, theturns-area product of the coils a2 _(x) to d2 _(x) could be different tothat of the coils a1 _(x) to d1 _(x), provided allowance is made forthis in the relative values of the resistors R_(1x) and R_(2x) orelsewhere in the circuit. Similarly, the turns-area product of the coilsa2 _(y) to d2 _(y) could be different to that of the coils a1 _(y) to d1_(y) provided suitable allowance is made elsewhere. Also, ifinterference from external sources is not probable in the circumstanceslikely to be encountered in use, the outer sets of coils, i.e. theorthogonal pairs of coils located on the circle of radius r₂ in FIG. 6,can be omitted. Further, since diametrically opposite sets of coils areprovided primarily to provide a larger signal and to further reduceexternal interference, as well as reducing errors due to movement of thecable from centre point P, the invention could be implemented with justtwo sets of coils at 90° spacing, e.g. the sets of coils at the 3o'clock and 6 o'clock positions of FIG. 6.

The invention is not limited to the embodiments described herein whichmay be modified or varied without departing from the scope of theinvention.

1-9. (canceled)
 10. An apparatus for measuring alternating current in aconductor, the apparatus comprising first and second coil means havingsubstantially the same turns-area product and substantially parallelaxes, the first and second coil means being located on the circumferenceof a notional circle with the first coil means having its axistangential to the circle and the second coil means having its axisextending radially of the circle, and third and fourth coil means alsohaving substantially the same turns-area product and substantiallyparallel axes, the third and fourth coil means being located on thecircumference of the notional circle close to the first and second coilmeans respectively, the third coil means having its axis extendingradially of the circle and the fourth coil means having its axistangential to the circle such that the first and third coil means form aclosely adjacent first pair of coil means with substantially orthogonalaxes and the second and fourth coil means form a closely adjacent secondpair of coil means with substantially orthogonal axes, the first tofourth coil means being mounted on a support means configured to allow aconductor to be introduced into the centre of the said circle with theaxis of the conductor normal to the plane containing the first to fourthcoil means, the apparatus further comprising means electricallyconnecting the first and second coil means in series in anti-phase andthe third and fourth coil means in series in anti-phase, and means forderiving the alternating current in the conductor as a function of thevoltages induced in the series-connected first and second coil means andthe series-connected third and fourth coil means.
 11. An apparatus asclaimed in claim 10, wherein each pair of orthogonal coil means has asubstantially identical pair of orthogonal coil means locatedsymmetrically on the diametrically opposite side of the centre of thefirst notional circle and having the same orientation as its symmetricalcounterpart, each coil means and its symmetrical counterpart beingconnected in series in the same phase.
 12. An apparatus as claimed inclaim 10, wherein all the coil means have substantially the sameturns-area product.
 13. An apparatus as claimed in claim 12, wherein theturns-area product of all the coil means are the same to within 1%. 14.An apparatus as claimed in claim 10, wherein each coil means is formedas conductive coil-forming tracks on at least one insulating substrateand the support means comprises an insulating motherboard, thesubstrates standing upright on the board and the coil-forming tracks onthe substrates being connected by conductive tracks on the motherboard.15. An apparatus as claimed in claim 14, wherein at least one pair oforthogonal coil means comprises a first insulating substrate bearing afirst coil-forming track defining one of said pair of orthogonal coilmeans and second and third insulating substrates disposed substantiallynormal to the first substrate and bearing second and third coil-formingtracks respectively, the second and third coil-forming tracks beingconnected together in series and together defining the other of saidpair of orthogonal coil means.
 16. An apparatus as claimed in claim 15,wherein the second and third coil-forming tracks have a combinedturns-area product substantially the same as the first coil-formingtrack.
 17. An apparatus as claimed in claim 15, wherein at least twocoil-forming tracks are formed on a common substrate.
 18. An apparatusas claimed in claim 10, further comprising fifth and sixth coil meanshaving substantially the same turns-area product and substantiallyparallel axes, the fifth and sixth coil means being located on thecircumference of a second notional circle concentric with, and having adiameter greater than, the first notional circle, the fifth coil meansbeing located radially outwardly of the first coil means and having itsaxis tangential to the second circle and the sixth coil means beinglocated radially outwardly of the second coil means and having its axisextending radially of the second circle, and seventh and eighth coilmeans also having substantially the same turns-area product andsubstantially parallel axes, the seventh and eighth coil means beinglocated on the circumference of the second notional circle close to thefifth and sixth coil means respectively, the seventh coil means havingits axis extending radially of the second circle and the eighth coilmeans having its axis tangential to the second circle such that thefifth and seventh coil means form a closely adjacent third pair of coilmeans with substantially orthogonal axes and the sixth and eighth coilmeans form a closely adjacent fourth pair of coil means withsubstantially orthogonal axes, the apparatus further comprising meanselectrically connecting the fifth and sixth coil means in series inanti-phase and the seventh and eighth coil means in series inanti-phase, the means for deriving the alternating current in theconductor deriving said current as a function of the voltages induced inthe series-connected first and second coil means, the series-connectedthird and fourth coil means, the series-connected fifth and sixth coilmeans, and the series-connected seventh and eighth coil means.
 19. Anapparatus as claimed in claim 18, wherein each pair of orthogonal coilmeans has a substantially identical pair of orthogonal coil meanslocated symmetrically on the diametrically opposite side of the centreof the first notional circle and having the same orientation as itssymmetrical counterpart, each coil means and its symmetrical counterpartbeing connected in series in the same phase.
 20. An apparatus as claimedin claim 18, wherein all the coil means have substantially the sameturns-area product.
 21. An apparatus as claimed in claim 20, wherein theturns-area product of all the coil means are the same to within 1%. 22.An apparatus as claimed in claim 18, wherein each coil means is formedas conductive coil-forming tracks on at least one insulating substrateand the support means comprises an insulating motherboard, thesubstrates standing upright on the board and the coil-forming tracks onthe substrates being connected by conductive tracks on the motherboard.23. An apparatus as claimed in claim 22, wherein at least one pair oforthogonal coil means comprises a first insulating substrate bearing afirst coil-forming track defining one of said pair of orthogonal coilmeans and second and third insulating substrates disposed substantiallynormal to the first substrate and bearing second and third coil-formingtracks respectively, the second and third coil-forming tracks beingconnected together in series and together defining the other of saidpair of orthogonal coil means.
 24. An apparatus as claimed in claim 23,wherein the second and third coil-forming tracks have a combinedturns-area product substantially the same as the first coil-formingtrack.
 25. An apparatus as claimed in claim 18, wherein at least twocoil-forming tracks are formed on a common substrate.